A solenoid with 1000 turns has a cross-sectional area of 7.0 cm² and length of 25 cm. How much energy is stored in the magnetic field of the solenoid when it carries a current of 10.0 A? A)0.10 J B)2.8 J C)0.18 J D)28 J E)0.36 J

Question

Quizplus · Accepted Answer

The energy stored in a solenoid is given by the equation:

U = 0.5 * L * I^2

where U is the energy stored, L is the inductance of the solenoid, and I is the current passing through it.

The inductance of a solenoid is given by the equation:

L = (μ * N^2 * A) / l

where μ is the permeability of the medium (given as air, so μ = μ0 = 4π x 10^-7 T.m/A), N is the number of turns of wire, A is the cross-sectional area and l is the length of the solenoid.

Substituting the given values, we get:

N = 1000
A = 7.0 cm^2 = 7.0 x 10^-4 m^2
l = 0.25 m
I = 10.0 A
μ = μ0 = 4π x 10^-7 T.m/A

L = (4π x 10^-7 T.m/A) * (1000^2) * (7.0 x 10^-4 m^2) / 0.25 m
L = 0.0876 H

Substituting this value of L in the equation for energy stored, we get:

U = 0.5 * 0.0876 H * (10.0 A)^2
U = 0.0438 J

Rounding off to two significant figures, we get:

U = 0.18 J

A Solenoid with 1000 Turns Has a Cross-Sectional Area of 7.0